In the rush to get data about how students are doing on tests, we need a little lesson in how to use mathematics and, specifically, percentages. A case in point is a recent article by The Washington Post, “In Fairfax, students score better on IB exams, while AP test results drop.” The article is about a decrease in the number of students taking Advanced Placement (AP) exams, an increase in number of students taking International Baccalaureate (IB) exams, and the performance of students on these exams. Quite literally, the author notes increasing minority participation, and misinterprets data about the resulting scores to create an (incorrect) declining success rate in the face of significant achievement and improvement on minority scores.

How is that possible?All it takes is a slight of hand about which data you cite. First, remember each student may take several exams for different topics. With that in mind, consider the changes from 2010 to 2013.

The number of students participating in AP exams went up five percent over those 3 years, while the number of students participating in IB exams increased 20 percent. The increases were even more significant for minority students on IB exams. As The Washington Post noted, “Among black students, the number of those taking IB exams increased by 36 percent, and the number of Hispanic students taking IB tests increased by 54 percent.” The number of exams taken by these students also increased. “The number of IB tests taken by black students increased by 29 percent while the number of tests administered to Hispanic students jumped by 81 percent. Scores for both ethnic groups also improved slightly.” Yet, the Post added, “The increase in the number of tests, however, did not lead to better scores overall for black or Hispanics, as the scores for both ethnic groups dropped slightly during that time.”

So which is it, did the scores improve slightly or did they drop slightly? It turns out that both statements are misleading. In fact, Fairfax County has seen phenomenal success.

Here’s a closer look at the IB data. In 2010, 63 percent of IB tests taken by black students were passed (4 or better). In 2013, only 61 percent of IB tests taken by black students were passed. Presumably this is the slight drop the Washington Post was referring to. But this small drop in percentage came along with a huge increase in participation, which means that despite the drop, black students are seeing increased pass rates. In 2010, black students passed just 348 IB exams, while in 2013, they passed 431 exams. That constitutes a 24 percent increase, hardly a “slight” improvement. And in case anyone poses the question, no the black population did not increase 24 percent in those 3 years. Similarly, in 2010, 70 percent of IB exams taken by Hispanics were passed, while that number dropped to 66 percent in 2013. Yet in 2010, Hispanics passed 468 tests while in 2013, they passed 796 tests, an increase by 70 percent. Asians and Whites also improved their performance: Asians passed 1,077 exams in 2010 and 1,244 in 2013, an increase by 15.5 percent, and Whites went from 2,621 exams passed to 3,294 exams, an increase of 25.6 percent.

The moral of the story here is that the percentages (the pass rates) are only considering the students as part of the group taking the tests. But that group has changed from 2010 to 2013, including a significantly larger population with some weaker students. That’s the reason that it’s irrelevant to report the percentage of the population passing the exams, and to compare over the years – they are percentages of different groups. In contrast, the sheer number of exams passed indicates tremendous progress in minority success (and non-minority success) at passing IB exams.

Now one could argue that these successes may indicate a general shift from AP exams to IB exams. The data show that the number of White and Other students decreased participating in taking AP exams, while the number of Asians, Blacks, and Hispanics students participating in AP exams increased. The number of actual AP exams taken also went up, for all demographics except Other. In sum, the IB exams were not sucking up students from the AP tests – participation in both types of exams is going up, as are the success rates.

Finally, what can be made of the claims by the Post that the scores went slightly up, and also went slightly down? Presumably, the Post was looking at different time periods. From 2012 to 2013, the average (mean) score on the IB exam went up for all ethnic groups, but from 2010 to 2013, they went down slightly for Blacks and Hispanics. These comparisons are meaningless, however, because of the large changes in number of exams being taken. For the record and as a matter of comparison the average scores for AP tests went slightly up for all groups except Whites from 2010 to 2013, and the number of students taking the AP exams did not increase as much as they did for the IB exams.

Overall, Fairfax County should note its success at increasing minority and non-minority participation and success in these advanced exams. And the kids who studied so hard and succeeded in these college level exams should be congratulated.

The Federal Reserve (the Fed) serves as the central bank in the United States of America. It was formed in 1913 to help create safer banking practices and promote financial stability. Today, the Fed’s stated goals are to “promote the objectives of maximum employment, stable prices, and moderate long-term interest rates.[1]”

(1) Maximum Employment:

When unemployment is high, the economy is not operating at its full potential, which can lead to lower production and output (lower GDP)

There is always going to be some level of unemployment in an economy (called the natural rate of unemployment)

Structural unemployment occurs when the skills an unemployed person has does not match the skills needed on the market

Frictional unemployment occurs when a worker is transitioning between jobs. The worker may have other job opportunities available to him, but chooses to be unemployed in order to hold out for a better offer (high salary, better benefits)

Hence, the Fed does not target an unemployment rate of zero, but it does seek to promote full employment, which occurs when the demand for labor equals the supply of labor

(2) Price stability (or low and stable inflation):

Inflation occurs when the supply of money increases relative to the demand for money

A rising price level creates uncertainty in the economy and makes it difficult to plan for the future

History suggests that inflation leads to lower economic growth

When prices are changing, it is hard to convey whether the change in the price of a particular good or service is due to changes in the demand for the good or because money was injected into the economy (i.e. inflation distorts prices)

According to the Fed, “When prices are stable and believed likely to remain so, the prices of goods, services, materials, and labor are undistorted by inflation and serve as clearer signals and guides to the efficient allocation of resources and thus contribute to higher standards of living.”[2]

(3) Interest Rate Stability:

According to the Fed, fluctuations in interest rates create uncertainty in the economy and make it harder to plan for the future

An increase in interest rates create large capital losses on long-term bonds and mortgages and can also lead to the failure of the financial institutions who hold them

How is the Federal Reserve Structured?

The Federal Reserve System is comprised of twelve district banks, headed by a Board of Governors. The seven members, who comprise the Board of Governors, are appointed by the President of the United States and confirmed by the U.S. Senate. Each Board member comes from a different district bank and serves a fourteen-year term. The seven members of the Board of Governors also sit on the twelve-member Federal Open Market Committee (FOMC), which sets the monetary policies of the country through influencing the availability of money and credit in the economy. The five other members of the FOMC serve as presidents of different district Reserve Banks, whose membership rotates annually. However, the President of the Federal Reserve Bank of New York is always a member of the Committee.

What tools does the Fed have at its disposal to promote its stated goals?

There are three main tools the Fed uses to promote maximum employment, price stability, and interest rate stability.

(1) Open Market Operations:

Open Market Operations are the most common way the Fed changes the monetary base, which is the amount of currency in circulation plus the total amount of reserves in the banking system. The Fed can change the monetary base by purchasing or selling bonds on the market. Open Market Purchases of bonds expand the monetary base; increase the money supply and lower short-term interest rates. Open Market Sales decrease the monetary base and the money supply and raise short-term interest rates.

Over more recent years, the Federal Reserve has focused its attention on affecting the federal funds rate, which is the interest rate on overnight loans that banks lend to one another. An open market purchase results in a larger quantity of reserves supplied on the market, which lowers the federal funds rate. Conversely, an open market sale leads to a decrease in the quantity of reserves supplied on the market, which raises the federal funds rate.

(2) Discount Rate:

Another method by which the Fed can affect the money supply is through setting the discount rate, which is the rate at which the Federal Reserve lends money to commercial banks. After the Federal Reserve Board set the discount rate, banks then have to decide whether or not they will borrow money from the Fed and how much they will borrow. Typically, a lower discount rate will lead to higher borrowing and an increase in the money supply, while a higher discount rate will discourage bank borrowing and decrease the money supply.

(3) The Reserve Requirement

The other method by which the Federal Reserve can affect the money supply is through changing the required reserve ratio, which dictates how much banks must hold in reserves based on the amount of checkable deposits the bank has. When the reserve requirement is increased, the bank needs to hold a larger quantity of reserves for a given amount of deposits. Increasing the reserve requirement decreases the money supply, while decreasing the reserve requirement increases it. Thus, the Fed can influence the level of deposits by setting the required reserve ratio (the percentage of deposits a bank must hold in their vaults.)

Who else affects the Money Supply?

There are three main entities that affect the money supply. Banks are able to affect the money supply by changing the amount of excess reserves they hold (the money they hold in reserves above the reserve requirement). When excess reserves are low (e.g. banks have made more loans to consumers and businesses), the money supply is higher with all other factors held constant. The money supply is also affected by how much a depositor decides to hold in currency, and by how much people borrow from banks.

How do we know if the Fed is hitting its targets?

Maximum Employment:

Since 1948, there have been large fluctuations in the Unemployment Rate, which means employment has not been stable over the historical time period.

Price Stability:

As mentioned before inflation arises when the supply of money increases relative to the demand for money, which leads to a rise in the general price level of goods and services over time. This lead economist Milton Friedman to declare, “Inflation is always and everywhere a monetary phenomena.”[3] When the general price level of goods and services increases, it becomes more expensive for an individual to buy the same goods he was previously buying. In other words, a dollar buys less.

The Consumer Price Index (CPI) is the most common method used to calculate inflation. The Bureau of Labor Statistics collects the data that go into the Index. The CPI is calculated by measuring the price of a “basket” of goods and services that are bought by the typical American household. The Index is supposed to measure typical American citizen’s cost of living and gives people an idea of how prices have risen or fallen over time.

Some of the categories that are tracked in the Index are food and beverages, housing, apparel, transportation, medical care, recreation, education and communications, and other goods and services, such as water and sewer services.

Since the Fed’s establishment in 1913, there have been several bouts of monetary instability. For instance, inflation skyrocketed starting in the early part of the 1970s. Interestingly, the United States abandoned the Gold Standard in 1971, which indicates that prices were much more stable under the Gold Standard than they have been since the abandonment of the Gold Standard.

Some economists are concerned that the CPI index does not fully capture inflation in the economy. First, the goods in the CPI index change from time to time, making it difficult to accurately document changes in prices since different baskets are actually being compared across time. In other words, the 1970 CPI basket is different from the 2012 basket. Economists are also concerned because it is unclear how the CPI adjusts for changes in the quality of goods and services.

While All Items CPI for All Urban Consumers (CPI-U) does incorporate energy and food prices in it’s measuring, the CPI index that is most commonly reported is the CPI-U for All Items Less Food and Energy.

Interest Rates:

As previously stated one of the goals of the Federal Reserve is to stabilize Interest Rates. First, it is important to understand what interest rates are and how they are determined. According to Economist Irving Fisher, “The rate of interest expresses a price in the exchange between present and future goods.”

Interest rates depend on individual’s time preference, i.e., how they value a dollar in the future relative to a dollar today. An individual who has high time preference focuses on the present and values goods and services today much higher than goods and services in the future, while an individual with low time preference puts more weight on the future.

There are several factors that can affect the interest rate. “Together intertemporal preferences and transformation opportunities determine the sequences of outputs and interest rates. “

When interest rates increase, the structure of production becomes less roundabout, redistributing productive resources away from producer goods toward consumer goods. When interest rates rise, higher rates of return in production are necessary to compete with financial instruments such as relatively higher-yielding government bonds.

When the Federal Reserve manipulates the Interest Rate it distorts the market and either production possibilities will not be realized (if the market interest rate is higher than the natural rate) or producers will invest in projects they otherwise would not have if the market interest rate is artificially low.

The Washington DC area (including Washington D.C., Northern Virginia, and Maryland) are disproportionately impacted by the expenditures of the federal government. As noted in a Washington Post article, “federal spending and procurement still represent about one-third of the region’s $443 billion economy.”[1]

Washington D.C. is the figurative “canary in the coal mine” when it comes to the economic consequences from the sequester – if the sequester is going to hurt anywhere, it will hurt the most in the D.C. metropolitan area.

One way to track the actual and expected economic consequences from any policy change is to track real estate (or housing) prices. House prices are, generally speaking, driven by local economic trends. Furthermore, housing prices reflect both a region’s current and expected future economic prospects. Weak income growth for local buyers, or the expectation that future buyers will experience weak income growth, is ultimately reflected in lower housing values. Therefore, changes in housing prices are a good metric to measure changes in both a region’s current and expected future economic prospects.

Housing data will lag behind events and the sequester is only weeks old. But, as of March 2013 there impact from the sequester is currently viewed as being mild, short-lived, or both. In short, the economic consequences from the sequester (thus far) has been not so much. Consider the following local trends. As the Washington Post’s Katy Orton pointed out the other day, “Median sale price of homes in Washington, D.C., hits record high”.

March median sales price by jurisdiction

2013

2012

YoY

DC metro

$372,500

$345,00

8%

Falls Church

$631,000

$458,300

37.7%

Arlington

$515,000

$509,450

1.1%

Alexandria

$487,500

$391,950

24.4%

District

$460,000

$405,000

13.6%

Fairfax County

$430,000

$398,500

7.9%

Fairfax City

$392,500

$443,750

-11.5%

Montgomery County

$375,000

$345,000

8.7%

Pr. George’s County

$176,500

$158,000

11.7%

Source: RealEstate Business Intelligence

Additionally, properties coming onto the market are staying on the market for a short period of time. The median days on market fell to 15 days last month, 26 days fewer than March 2012. It is the shortest days on market for any month since September 2005.

Showcasing two voices from both sides of the issue, Larry Kudlow has argued that while:

President Barack Obama may be backing away from his doomsday spending-cut predictions as the sequester goes into place…the new party line is that while there will be no impact in the first few days, there’ll be a slow, downward slump after that.

What, are we to believe that lower spending and smaller government damage the economy? Doesn’t that run counter to virtually every reasonably objective study in recent years—including ones from a number of U.S. academics and the OECD in Europe—that describe how countries with lower government spending grow more, and how countries with higher government spending grow less?

However you calculate the sequester spending cuts, and however uneven they may be, the reality is that the sequester at least moves the ball in the right direction. I maintain that by reducing the government spending share of gross domestic product, the sequester is pro-growth.[1]

On the other side of the debate, Jon Favreau on The Daily Beast details a parade of horrific outcomes wrought by the sequestration:

One month and 5 billion cable hits on White House tours later, a flurry of great reportingis allowing us to answer for ourselves the question of whether President Obama has “cried wolf.” If we want, we can ask the Americans who are losing their jobs at military bases in Tennessee, Illinois, and Virginia. We can ask the health-care employees facing layoffs in New York, or the contractors in Oklahoma, or the teachers in Iowa, or the workers cleaning up nuclear waste in Washington. We can ask the children in Ohio and Pennsylvania who will no longer receive the early education that Head Start provides. We can ask the scientists and researchers at Duke and the University of Florida who must end their pursuit of discoveries that could change or save lives. We can ask the hungry families in Utah who can no longer rely on the local food pantry, the disabled tenants in California who will lose their housing vouchers, the elderly cancer patients in South Carolina who are being denied their chemotherapy treatment, or the 39-year-old Army veteran in Maryland who believes the only way to survive his pay cut is with another combat deployment.

1. Air Force base jobs lost in Tullahoma, Tenn. — The Aerospace Testing Alliance announced it is cutting 128 of 1,809 civilian jobs at Arnold Air Force Base in Tullahoma starting April 19. It has also put in place a 20 percent pay cut and weekly furloughs for workers at a research facility.

4. Food pantry closed in Murray, Utah. — The Salt Lake Community Action Program closed its food pantry, one of five locations that serve more than 1,000 people every month. Executive Director Cathy Hoskins told The Huffington Post that in addition to the closure, the organization has stopped paying into employees’ retirement plans, won’t fill an open job and told some staffers to take a week’s unpaid leave. “I’ve had one person retire, we’re not replacing them. We’re not doing any hiring at all,” Hoskins said. “We’re trying very hard to boost our volunteers, but this is hard work working in a pantry. And if you get a volunteer, usually it’s a short-term volunteer because it’s just very very difficult work. … No raises, no increases, none of that stuff. We’re cutting everything we possibly can.” [Link]

27. Less camping in Connell, Wash. — Scooteney Park has remained closed to campers because of sequestration. Day use remains intact.

29. Air show cancelled in Rapid City, S.D. — Officials at Ellsworth Air Force Base have cancelled the Dakota Thunder air show this year. It has been held every few years for decades at the base.

However, assessing the value of the closed programs – and perhaps many people would value a food pantry above air shows or campground availability – requires an understanding of what else is foregone. The debate over the sequester cannot be adequately settled without an understanding of the private resources foregone in order to maintain the public expenditures that have been reduced. Going forward, such a trade-off is the key to understanding the actual net economic impact from the sequester.

Regardless of one’s position, unless the current policy course is changed, the effects of the sequestration will continue to shake out over the next couple of weeks and months. And, it may be a little premature to, pace Mark Twain, proclaim that the rumors of the “sequestration apocalypse” have been greatly exaggerated.

However, if squeezing $88 billion, or 2.4%, out of a $3.7 trillion budget is this difficult, even with the motivation of a $16.8 trillion dollar national debt hanging over our heads, then the future $123 trillion unfunded liabilities and debt will be even more problematic.

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Dr. Boudreaux over a Café Hyack highlights some great “shocking stats” inherent in a Charles Krauthammer column the other day. Krauthammer’s column (“The Obama budget and the appearance of reform,” April 12), addresses Obama’s new budget proposal wherein Krauthammer notes that the actual budget deficit reduction in the budget proposal over a decade was a scant $0.6 trillion out of a total spending of $46.5 trillion.

The effects on the debt, Boudreaux notes, will be “negligible.” In fact: “The year in which the amount of Uncle Sam’s debt held by the pubic will reach its lowest level under the Obama plan…the amount of such debt will be 73 percent of GDP – just what it is today and nearly double (!) the historical average of 37 percent” (see his full post here)

What, in the end, is most shocking is the amount of hock our administration is tacitly accepting and furthermore, given we haven’t had a budget in years, that this is the best they can come up with propose after all this time.

Mathematics used incorrectly can ruin people’s lives, pointed out in a recent oped in the New York Times. Two key mathematical themes come into play for these cases of justice. First, bad luck can look like criminal behavior if one simply calculates the probability that some unlikely event (such as several patients dying, or several children in one person’s care passing away by SIDS) occurs. However, the mathematics of bad luck suggests that someone will be very unlucky. Analogously – it’s extremely unlikely that any particular person will win the lottery, but it’s very likely that someone will win. It would be nonsensical to harass the winner figuring foul play must be at issue, since the odds he would win are so slim. Second, repeating independent biological tests on evidence strengthens a conclusion, rather than weakens it – a statistical conclusion only tells you how likely you are to see specific data under certain assumptions. The more data you have, the more sure you can be of your statistical conclusion.

Conclusion? Without other evidence, we should assume that an accused murderer is the unluckiest of everyone to whom the bad luck might have happened – and only use mathematics to calculate the probability that this bad luck might have happened to someone rather than to this particular person. And multiple DNA tests on different samples, or even the same sample, of evidence makes a stronger case as to whether the resulting DNA analysis suggests guilt or innocence.